Chapter 10.7, Problem 18AYU

In Problems 7-26, graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.

$x=t^{3/2}+1$, $y=\sqrt{t}$; $t\ge 0$

To determine

To find:

a. The rectangular equation of the curve.

Answer to Problem 18AYU

$x=y³+1$, $y\ge 0$

Explanation of Solution

Given:

$x=t^{3/2}+1,y=\sqrt{t}; t\ge 0$

Calculation:

$x=t^{3/2}+1, y=\sqrt{t},$$y=t^{3/2}; t\ge 0$

$x=\sqrt{t^3}+1, t\ge 0$

$x=y³+1,y\ge 0$

To determine

To graph:

b. $x=t^{3/2}+1, y=\sqrt{t}; t\ge 0$ verify with the graph of rectangular equation of the curve.

Answer to Problem 18AYU

Explanation of Solution

Given:

$x=t^{3/2}+1, y=\sqrt{t}; t\ge 0$

Graph:

The graph of $x=t^{3/2}+1, y=\sqrt{t}; t\ge 0$ is plotted.

The graph of $xy=1\left\{\text{log}x\ge 0\right\}$ is plotted.

Graph 1 represents the graph of: $x=t^{3/2}+1, y=\sqrt{t}; t\ge 0$ plotted in parametric mode and the orientation is shown.

The rectangular equation of the curve is calculated. Graph 2 represents the curve of the rectangular equation $x=y³+1,y\ge 0$.

Both the equation represents the same graph and orientation. Hence it is verified.